A method for evaluating the insulation status of high-voltage generator stator windings

Abstract

The present invention discloses a method for evaluating the insulation status of a high-voltage generator stator winding, relating to the technical field of power systems. The method comprises: establishing an extended Debye model for the insulation of a high-voltage generator stator winding; performing modal decomposition on the depolarization current time series of the high-voltage generator stator winding based on a dynamic modal decomposition algorithm to obtain modes of various orders with different physical meanings; performing sparse processing on each order mode based on a fast iterative shrinkage threshold algorithm (FISTA) to separate dominant modes from false modes, and using the dominant modes to solve the extended Debye model to achieve accurate collaborative identification of the number of model branches and branch parameters; and based on the solution results, using preset model parameters to perform simulations and thermal aging experiments. The present invention solves the problems of existing methods in that the number of branches of the extended Debye model for the insulation of a high-voltage generator stator winding is difficult to determine, the physical meaning of the model is unclear, and the model parameter identification method has poor noise immunity.

Description

Technical Field

[0001] The present invention relates to the technical field of power systems, and in particular to a method for evaluating the insulation state of a high-voltage generator stator winding. Background Art

[0002] Large high-voltage generator sets are a core component of modern power systems, and their reliable and stable operation directly determines the safe and stable operation of the power system. During operation, the stator windings of high-voltage generators are subjected to electrical, thermal, mechanical, and environmental stresses, causing rapid insulation aging, which can easily lead to abnormal operation or even failure. A sudden failure of the generator set would result in enormous economic losses, with disastrous consequences. Therefore, accurately assessing the insulation condition of high-voltage generator stator windings is crucial to ensuring the safe and stable operation of the power system.

[0003] Currently, researchers using the Polarization and Depolarization Current (PDC) method to assess insulation condition follow these steps: equivalently modeling the insulation's time-domain dielectric response characteristics—establishing an extended Debye model of the insulation—combining this with the PDC test current to obtain the model's specific parameters, and then determining the insulation condition based on the parameter amplitudes and variations. Therefore, the two keys to using this method to diagnose the insulation condition of high-voltage generator stator windings are: establishing an extended Debye model that conforms to the epoxy-mica composite insulation system; and accurately identifying the model parameters using PDC test data.

[0004] However, existing methods have difficulty in determining the number of branches in the extended Debye model of high-voltage generator stator winding insulation, the physical meaning of the model is unclear, and the model parameter identification method has poor noise resistance. Summary of the Invention

[0005] In response to the above-mentioned deficiencies in the prior art, the present invention provides a method for evaluating the insulation status of a high-voltage generator stator winding, which solves the problems that the existing method is difficult to determine the number of branches of the extended Debye model of the high-voltage generator stator winding insulation, the physical meaning of the model is unclear, and the model parameter identification method has poor noise resistance.

[0006] In order to achieve the above-mentioned object of the invention, the technical solution adopted by the present invention is: a method for evaluating the insulation status of a high-voltage generator stator winding, comprising the following steps:

[0007] S1: Establish an extended Debye model for high-voltage generator stator winding insulation;

[0008] S2: Based on the dynamic modal decomposition algorithm, the depolarization current time series of the high-voltage generator stator winding is modally decomposed to obtain various modes with different physical meanings;

[0009] S3: Based on the fast iterative shrinkage threshold algorithm FISTA, each mode is sparsified to separate the dominant mode from the false mode. The dominant mode solution is used to expand the Debye model and achieve accurate collaborative identification of the number of model branches and branch parameters.

[0010] S4: Based on the solution results, simulation and thermal aging experiments are performed using preset model parameters to complete the insulation status evaluation of the high-voltage generator stator winding.

[0011] Furthermore, the depolarization current of the extended Debye model in S1 is expressed as:

[0012]

[0013] τ i =R i ×C i

[0014] Among them, i depol is the depolarization current, U0 is the polarization voltage, R0 is the insulation resistance, R i is the resistance of branch i, n is the number of relaxation branches, t is the time, τ i is the relaxation time constant, A i is the current amplitude of branch i, t p is the polarization time, C i is the capacitance of branch i.

[0015] Furthermore, the step S2 includes the following sub-steps:

[0016] S21: Construct the depolarization current time series into a Hankel matrix, the formula is:

[0017]

[0018] Where C is the Hankel matrix, c(·) is the depolarization current sequence, a is the number of rows of the Hankel matrix, b is the number of columns of the Hankel matrix, and N is the number of depolarization current sampling points;

[0019] S22: Based on the dynamic mode decomposition algorithm, the first b-1 columns and the last b-1 columns of the Hankel matrix are taken to form a lead matrix and a lag matrix. The relationship between the lead matrix and the lag matrix is:

[0020] C2=KC1+ε

[0021] Where C1 is the leading depolarization current matrix, C2 is the lagging depolarization current matrix, K is the Koopman operator, and ε is the residual matrix;

[0022] S23: Perform singular value decomposition on the leading depolarization current matrix, and perform low-rank approximation on the Koopman operator based on the decomposition result, and construct a low-rank operator in the low-rank space;

[0023] S24: Solve the eigenvalues ​​and eigenvectors of the low-rank operator, and based on the solution results, obtain the various modes of different physical meanings of the extended Debye model of the stator winding insulation of the high-voltage generator.

[0024] Furthermore, in S23, the leading depolarization current matrix is ​​subjected to singular value decomposition, and the formula is:

[0025] C1=UΣV *

[0026] Where U is the left singular matrix, Σ is the singular value matrix, V is the right singular matrix, and the superscript * indicates the complex conjugate transpose of the matrix;

[0027] Construct a low-rank Koopman operator in a low-rank space, the formula is:

[0028]

[0029] Among them, K r is a low-rank operator, U r is the left singular matrix U, V after rank truncation r is the left singular matrix V after rank truncation, is the singular value matrix Σ after rank truncation.

[0030] Furthermore, in S24, the eigenvalue and eigenvector of the low-rank operator are solved, and the formula is:

[0031] K r W=WΛ

[0032] Where W is K r The eigenvector matrix of K r The diagonal matrix of eigenvalues;

[0033] The modes of different physical meanings of the extended Debye model of the high-voltage generator stator winding insulation are:

[0034]

[0035] Where Φ is the modal vector, φ1, φ2,…, φ r For modal.

[0036] Furthermore, the step S3 includes the following sub-steps:

[0037] S31: Establish the initial amplitude coefficients of each mode;

[0038] S32: Based on the initial amplitude coefficient, the fast iterative shrinkage threshold algorithm FISTA and the penalty function are used for sparsification to separate the dominant mode from the false mode;

[0039] S33: Based on the separated dominant modes, the parameters of the extended Debye model are calculated to achieve accurate collaborative identification of the number of model branches and branch parameters. The formula is:

[0040]

[0041] Among them, τ m is the time constant of branch m, T s is the sampling time interval of PDC test, λ1,λ2,…,λ m is the eigenvalue corresponding to the dominant mode, A1, A2, ..., A m is the amplitude coefficient of branch m.

[0042] Furthermore, the S31 includes the following sub-steps:

[0043] S311: Establish the expression of the leading depolarization current matrix including the initial amplitude coefficient, the formula is:

[0044]

[0045] Among them, C1 is the leading depolarization current matrix, D α is the initial amplitude coefficient matrix, V and is the Vandermonde matrix containing the main insulation relaxation characteristics, the superscript T is the transpose of the matrix, α1,α2,…,α r are the initial amplitude coefficients of each mode, λ1,λ2,…,λ r is the eigenvalue corresponding to each mode;

[0046] S312: Obtain the reconstruction error caused by the leading depolarization current matrix including the initial amplitude coefficient, solve the reconstruction error, and complete the establishment of the initial amplitude coefficient of each order mode. The reconstruction error is:

[0047]

[0048] q=diag(V and VΣ * W) T

[0049] s=tra(Σ * Σ)

[0050] α=[α1α2…α r ] T

[0051] Among them, J(·) is the reconstruction error, α is the vector composed of the amplitude coefficients of each order mode, ||·|| F is the Frobenius norm, tra(·) is the trace of the matrix, P is the first parameter, q is the second parameter, s is the third parameter, and diag(·) is the column vector formed by taking the main diagonal elements of the matrix;

[0052] The vector α formed by the amplitude coefficients of each order mode is solved as follows:

[0053] α=P -1 q.

[0054] Furthermore, the S32 includes the following sub-steps:

[0055] S321: Using the 1-norm as the regularization penalty function, the objective function H for optimizing the initial amplitude coefficients of each mode is established. The formula is:

[0056]

[0057] S322: The fast iterative shrinkage threshold algorithm FISTA is used to iteratively solve the objective function of optimizing the initial amplitude coefficients of each mode to eliminate false modes and achieve separation of dominant modes from false modes.

[0058] Furthermore, in S322, the fast iterative shrinkage threshold algorithm FISTA is used to iteratively solve the objective function of optimizing the initial amplitude coefficients of each mode, including the following steps:

[0059] S3221: Set α=P -1 The α calculated by q is set as the initial value of the iteration α0, the initial value of the momentum term y1 = α0, the initial value of the momentum acceleration parameter t1 = 1, and the step size L is the Lipschitz constant of the objective function;

[0060] S3222: Perform gradient descent solution, the formula is:

[0061]

[0062] Among them, α' k is the value of α at the kth iteration, is the regularization penalty function f(α) at ​​point y k The gradient at y k is the momentum variable;

[0063] S3223: To α' k Perform soft threshold shrinkage to obtain the α of the next iteration k for:

[0064]

[0065] Where Shrink(·) is the soft threshold function, and ε0 is the threshold of the soft threshold operation;

[0066] S3224: Update momentum acceleration parameter t k for:

[0067]

[0068] Among them, t k+1 is the updated momentum acceleration parameter t k ;

[0069] S3225: According to α k and t k+1 Update the momentum variable y for the next step k+1 for:

[0070]

[0071] S3226: Momentum variable y based on the next step k+1 , return to step S3222 and iterate until the convergence condition is reached, and then stop iterating. The convergence condition is:

[0072] ||α k -α k-1 ||≤ε end

[0073] Among them, ε end is the preset convergence threshold.

[0074] Furthermore, in S322, in order to eliminate the false modes, the amplitudes of the false modes are set to zero, so that each dominant mode corresponds to the branch of the extended Debye model in a one-to-one manner. The formula is:

[0075] minJ(α),stE T α=0

[0076] Where E is a matrix whose column vectors are unit vectors.

[0077] The beneficial effects of the present invention are as follows: the present invention proposes an evaluation method based on sparse enhanced dynamic decoupling of depolarization current, which can automatically determine the number of branches of the extended Debye model of the main insulation of the stator winding of a high-voltage generator. The physical meaning is clear, and the method has strong robustness and excellent identification accuracy. First, the modal decomposition of the depolarization current time series is performed based on the dynamic mode decomposition algorithm (DMD) to obtain modes of various orders with different physical meanings. Subsequently, the fast iterative shrinkage threshold algorithm FISTA is introduced to perform sparse processing on the modes of various orders, separate the dominant modes from the false modes, and use the dominant modes to solve the model parameters, thereby realizing the automatic determination of the branches of the extended Debye model and the accurate identification of the model parameters. Finally, the accuracy of the method is verified by simulation experiments with preset model parameters, and the feasibility of the method is verified by performing insulation state evaluation and microscopic performance characterization on stator bars under different thermal aging conditions. BRIEF DESCRIPTION OF THE DRAWINGS

[0078] Figure 1 The present invention is a flow chart of a method for evaluating the insulation condition of a high-voltage generator stator winding.

[0079] Figure 2 Wiring diagram for PDC test.

[0080] Figure 3 Schematic diagram of the expanded Debye model.

[0081] Figure 4 This is the identification result diagram when there is 5% noise.

[0082] Figure 5 Schematic diagram of stator bar sample dimensions. DETAILED DESCRIPTION

[0083] The present invention will be further described below with reference to the accompanying drawings and specific embodiments.

[0084] like Figure 1 As shown, a method for evaluating the insulation status of a high-voltage generator stator winding comprises the following steps:

[0085] S1: Establish an extended Debye model for high-voltage generator stator winding insulation;

[0086] S2: Based on the dynamic modal decomposition algorithm, the depolarization current time series of the high-voltage generator stator winding is modally decomposed to obtain various modes with different physical meanings;

[0087] S3: Based on the fast iterative shrinkage threshold algorithm FISTA, each mode is sparsified to separate the dominant mode from the false mode. The dominant mode solution is used to expand the Debye model and achieve accurate collaborative identification of the number of model branches and branch parameters.

[0088] S4: Based on the solution results, simulation and thermal aging experiments are performed using preset model parameters to complete the insulation status evaluation of the high-voltage generator stator winding.

[0089] The process of using PDC method to evaluate the insulation condition of high voltage generator stator bars is as follows: Figure 2 In the test circuit shown, the slot of the wire rod is tightly fitted with copper foil and then connected to the test pole. Shielding rings are used on both sides of the copper foil to shield the influence of surface current. Polarization voltage U0 is applied to the copper conductor of the wire rod to polarize the main insulation of the wire rod. During the test, the time domain dielectric response characteristics of the main insulation of the high-voltage generator stator winding can be equivalent to a multi-branch RC circuit consisting of a series of series-parallel resistors and capacitors, which is called the extended Debye model, as shown in Figure 3 shown.

[0090] Each branch in the model represents a type of relaxation or conduction process. R0 is the insulation resistance, which represents the conduction process of the main insulation under the action of the electric field; C0 is the geometric capacitance, which represents the sum of the instantaneous polarization process of the main insulation. Since the instantaneous polarization process takes a very short time, the measurement equipment cannot record the response process; R i 、C i The series branches represent various relaxation processes within the main insulation. Equilibrium is applied to the time-domain dielectric response characteristics of the main insulation of the high-voltage generator stator winding, yielding the following depolarization current.

[0091] The depolarization current of the extended Debye model in S1 is expressed as:

[0092]

[0093] τ i =R i ×C i

[0094] Among them, i depol is the depolarization current, U0 is the polarization voltage, R0 is the insulation resistance, R i is the resistance of branch i, n is the number of relaxation branches, t is the time, τ i is the relaxation time constant, A i is the current amplitude of branch i, t p is the polarization time, C i is the capacitance of branch i.

[0095] Therefore, to use the PDC method to evaluate the insulation condition of high-voltage generator stator bars, we must first determine the number of relaxation branches n with clear physical meaning. On this basis, the insulation resistance R0 and branch relaxation strength coefficient A are accurately calculated using the test data. i and the relaxation time constant τ i , only then can the insulation status evaluation of the high-voltage generator stator bars be realized.

[0096] To address the unclear physical meaning of the branch number in the extended Debye model, this paper introduces the DMD algorithm to perform modal decomposition on the depolarization current time series, obtaining physically clear modes of each order. Subsequently, the fast iterative shrinkage threshold algorithm (FISTA) is introduced to perform sparse enhancement on each order mode, improving the robustness of the identification method and separating dominant modes from spurious modes. The dominant modes are then used to solve the extended Debye model, achieving the precise collaborative identification of the branch number and branch parameters of the extended Debye model for high-voltage generator stator winding insulation.

[0097] The S2 includes the following steps:

[0098] S21: Construct the depolarization current time series into a Hankel matrix, the formula is:

[0099]

[0100] Where C is the Hankel matrix, c(·) is the depolarization current sequence, a is the number of rows of the Hankel matrix, b is the number of columns of the Hankel matrix, and N is the number of depolarization current sampling points;

[0101] S22: Based on the dynamic mode decomposition algorithm, the first b-1 columns and the last b-1 columns of the Hankel matrix are taken to form a lead matrix and a lag matrix. The relationship between the lead matrix and the lag matrix is:

[0102] C2=KC1+ε

[0103] Where C1 is the leading depolarization current matrix, C2 is the lagging depolarization current matrix, K is the Koopman operator, and ε is the residual matrix;

[0104] S23: Perform singular value decomposition on the leading depolarization current matrix, and perform low-rank approximation on the Koopman operator based on the decomposition result, and construct a low-rank operator in the low-rank space;

[0105] S24: Solve the eigenvalues ​​and eigenvectors of the low-rank operator, and based on the solution results, obtain the various modes of different physical meanings of the extended Debye model of the stator winding insulation of the high-voltage generator.

[0106] In S23, the leading depolarization current matrix is ​​subjected to singular value decomposition, and the formula is:

[0107] C1=UΣV *

[0108] Where U is the left singular matrix, Σ is the singular value matrix, V is the right singular matrix, and the superscript * indicates the complex conjugate transpose of the matrix;

[0109] Construct a low-rank Koopman operator in a low-rank space, the formula is:

[0110]

[0111] Among them, K r is a low-rank operator, U r is the left singular matrix U, V after rank truncation r is the left singular matrix V after rank truncation, is the singular value matrix Σ after rank truncation.

[0112] The depolarization test of a high-voltage generator stator winding typically lasts 10-30 minutes. To ensure test accuracy, the test sampling rate is usually no less than 20Hz. This results in an extremely large amount of data for a single test. Directly solving the operator K is time-consuming and is not conducive to rapid dynamic decoupling analysis of the depolarization current data on site.

[0113] In order to speed up the calculation and prevent the calculation from diverging, the Koopman operator is approximated by low rank. Since the magnitude of the noise in the field test is smaller than the magnitude of the depolarization current, the rank truncation operation eliminates the influence of various test noises in the field test to a certain extent, and improves the robustness of this method. After a large number of test analyses, it is found that the steady-state value of the depolarization current is used as the rank truncation threshold and truncation can meet the subsequent calculation requirements, avoiding the problem of insufficient prior knowledge of on-site maintenance personnel and lowering the threshold for use of this method. Assuming that the rank truncation is r, a low-rank operator K that can reflect the characteristics of the A matrix is ​​constructed in the low-rank space. r .

[0114] In S24, the eigenvalues ​​and eigenvectors of the low-rank operator are solved, and the formula is:

[0115] K r W=WΛ

[0116] Where W is K r The eigenvector matrix of K r The diagonal matrix of eigenvalues;

[0117] The modes of different physical meanings of the extended Debye model of the high-voltage generator stator winding insulation are:

[0118]

[0119] Where Φ is the modal vector, φ1, φ2,…, φ r For modal.

[0120] Dynamic decoupling of the depolarization current is achieved based on the DMD algorithm. However, the modes of each order after rank truncation still contain false modes caused by noise. In order to improve the robustness of the algorithm and achieve the unique determination of the number of Debye branches for the insulation expansion of the stator winding of the high-voltage generator, the present invention uses the fast iterative shrinkage threshold algorithm FISTA to screen the amplitude coefficients of each order mode, separate the dominant mode from the false mode, and achieve accurate collaborative identification of the number of model branches and branch parameters.

[0121] The S3 includes the following sub-steps:

[0122] S31: Establish the initial amplitude coefficients of each mode;

[0123] S32: Based on the initial amplitude coefficient, the fast iterative shrinkage threshold algorithm FISTA and the penalty function are used for sparsification to separate the dominant mode from the false mode;

[0124] S33: Based on the separated dominant modes, the parameters of the extended Debye model are calculated to achieve accurate collaborative identification of the number of model branches and branch parameters. The formula is:

[0125]

[0126] Among them, τ m is the time constant of branch m, T s is the sampling time interval of PDC test, λ1,λ2,…,λ m is the eigenvalue corresponding to the dominant mode, A1, A2, ..., A m is the amplitude coefficient of branch m.

[0127] The S31 includes the following sub-steps:

[0128] S311: Establish the expression of the leading depolarization current matrix including the initial amplitude coefficient, the formula is:

[0129]

[0130] Among them, C1 is the leading depolarization current matrix, D α is the initial amplitude coefficient matrix, V and is the Vandermonde matrix containing the main insulation relaxation characteristics, the superscript T is the transpose of the matrix, α1,α2,…,α r are the initial amplitude coefficients of each mode, λ1,λ2,…,λ r is the eigenvalue corresponding to each mode;

[0131] S312: Obtain the reconstruction error caused by the leading depolarization current matrix including the initial amplitude coefficient, solve the reconstruction error, and complete the establishment of the initial amplitude coefficient of each order mode. The reconstruction error is:

[0132]

[0133] q=diag(V and VΣ * W) T

[0134] s=tra(Σ * Σ)

[0135] α=[α1α2…α r ] T

[0136] Among them, J(·) is the reconstruction error, α is the vector composed of the amplitude coefficients of each order mode, ||·|| F is the Frobenius norm, tra(·) is the trace of the matrix, P is the first parameter, q is the second parameter, s is the third parameter, and diag(·) is the column vector formed by taking the main diagonal elements of the matrix;

[0137] The vector α formed by the amplitude coefficients of each order mode is solved as follows:

[0138] α=P -1 q.

[0139] By establishing the initial amplitude coefficients of each mode, it is convenient to use the amplitude coefficients to screen the modes later.

[0140] Based on the determination of the initial amplitude coefficient, in order to accurately screen the dominant modes representing the insulation relaxation characteristics of the high-voltage generator stator winding, the present invention introduces a penalty function to perform sparse enhancement iterative calculations, minimizing the deviation between the dominant modes and modes containing key system information and the dynamic oscillation information contained in the leading depolarization current matrix C1. In other words, the dominant modes and modes are used to achieve a hierarchical description of the leading depolarization current matrix C1. The improved optimization problem is:

[0141] minJ(α)+γf(α)

[0142] Among them, γ is the regularization parameter, and its size represents the sparsity of the penalty function. The larger the value, the higher the sparsity. f(α) is the regularization penalty function. Commonly used regularization penalty functions are 1-norm and 2-norm.

[0143] In order to save time in evaluating the insulation status of stator windings at the maintenance site, the 1-norm is selected as the regularization penalty function after comprehensively considering the calculation time and calculation accuracy.

[0144] The S32 includes the following sub-steps:

[0145] S321: Using the 1-norm as the regularization penalty function, the objective function H for optimizing the initial amplitude coefficients of each mode is established. The formula is:

[0146]

[0147] S322: The fast iterative shrinkage threshold algorithm FISTA is used to iteratively solve the objective function of optimizing the initial amplitude coefficients of each mode to eliminate false modes and achieve separation of dominant modes from false modes.

[0148] By solving the objective function H, we can obtain the optimal solution for α, effectively eliminating false modes caused by various noises in the maintenance field test and improving the robustness of the algorithm. This solution uses FISTA to iteratively solve formula H to eliminate false modal information in the system.

[0149] In S322, the fast iterative shrinkage threshold algorithm FISTA is used to iteratively solve the objective function of optimizing the initial amplitude coefficients of each mode, including the following steps:

[0150] S3221: Set α=P -1 The α calculated by q is set as the initial value of the iteration α0, the initial value of the momentum term y1 = α0, the initial value of the momentum acceleration parameter t1 = 1, and the step size L is the Lipschitz constant of the objective function;

[0151] S3222: Perform gradient descent solution, the formula is:

[0152]

[0153] Among them, α' k is the value of α at the kth iteration, is the regularization penalty function f(α) at ​​point y k The gradient at y k is the momentum variable;

[0154] S3223: To α' k Perform soft threshold shrinkage to obtain the α of the next iteration k for:

[0155]

[0156] Where Shrink(·) is the soft threshold function, and ε0 is the threshold of the soft threshold operation;

[0157] S3224: Update momentum acceleration parameter t k for:

[0158]

[0159] Among them, t k+1 is the updated momentum acceleration parameter t k ;

[0160] S3225: According to α k and t k+1 Update the momentum variable y for the next step k+1 for:

[0161]

[0162] S3226: Momentum variable y based on the next step k+1 , return to step S3222 and iterate until the convergence condition is reached, and then stop iterating. The convergence condition is:

[0163] ||α k -α k-1 ||≤ε end

[0164] Among them, ε end is the preset convergence threshold.

[0165] When the optimal solution of α is obtained, in order to more intuitively screen the dominant mode, the convex optimization problem shown in the following formula is introduced, and the amplitude of the false mode is set to zero.

[0166] In the step S322, the amplitude of the false mode is set to zero to eliminate the false mode, so that each dominant mode corresponds to the branch of the extended Debye model. The formula is:

[0167] minJ(α),stE T α=0

[0168] Where E is a matrix whose column vectors are unit vectors.

[0169] The above-mentioned sparse process based on the fast iterative shrinkage threshold algorithm FISTA achieves the optimal amplitude coefficient α sp The accurate construction of provides a basis for the selection of dominant modes. sp Not 0, corresponding to the false mode α sp The dominant mode of the stator winding main insulation dielectric response is accurately screened based on the characteristic of zero. Based on the screening results, the different physical meanings of the extended Debye model of the high-voltage generator stator winding insulation are recalculated to obtain the parameters of the extended Debye model of the stator winding main insulation.

[0170] In one embodiment of the present invention, in order to verify the accuracy of the above algorithm, this embodiment uses MATLAB to generate the depolarization current time series of the three branches for branch identification, and the parameter settings of each branch are shown in Table 1. At the same time, in order to simulate the strong noise environment faced during on-site inspection, random noise is added to the three-branch simulation current data to simulate the interference in the on-site test. The depolarization current shows an exponential decay trend over time, so the signal-to-noise ratio at the end of the current is lower. This embodiment introduces random noise with a ratio of 1%, 3%, and 5% of the maximum noise amplitude to the current amplitude at the last moment of the depolarization current. In order to quantify the branch identification effect of this algorithm, the determination coefficient R is introduced. 2 and mean absolute percentage error MAPE.

[0171] Table 1 MATLAB simulation depolarization current branch parameters

[0172]

[0173] Coefficient of determination R 2 It is a statistical indicator used to evaluate the goodness of fit between the identified data and the original data. Its calculation formula is as follows. The value range is 0-1. R 2 The larger it is, the better the fitting effect is.

[0174]

[0175] Among them, c(i) is the measured current data, To identify current data.

[0176] The mean absolute percentage error (MAPE) is a statistical indicator that measures the accuracy of a prediction model. It represents the absolute percentage error between the predicted value and the actual value. The calculation formula is as follows. The smaller the MAPE value, the smaller the difference between the identification result and the original data.

[0177]

[0178] The depolarization current data under different noise conditions were identified, and the branch parameter results were shown in Table 2. Figure 4 The identification results for 5% noise are shown. As can be seen from the table and figure, as the noise amplitude gradually increases, the error in the identification results of this algorithm gradually increases. However, even in the 5% noise condition, the accuracy and robustness of this algorithm remain excellent, making it highly feasible to use this algorithm for diagnosing the insulation condition of stator windings in industrial sites.

[0179] Table 2 Identification results under different noise conditions

[0180]

[0181] In order to verify the practical application effect of the algorithm proposed in the present invention, a stator wire rod thermal aging verification test was carried out in the laboratory. The test sample selected the newly produced high-voltage generator stator wire rod with a rated voltage of 15.75kV and a rated capacity of 312MW. Its insulation grade is F class, the main insulation is epoxy resin-mica-glass fiber system, and the manufacturing process is low-glue vacuum pressure impregnation (VPI). During the experiment, a short wire rod sample was cut from the low-resistance paint section in the middle of the complete stator wire rod sample, and the sample length was 50cm. A 7cm low-resistance anti-corona tape was peeled off at both ends of the cut short sample, and a 0.3mm thick high-resistance anti-corona paint was applied at a distance of 2cm to 7cm from both ends. Subsequently, a 0.3mm thick low-resistance anti-corona paint was applied at a distance of about 5cm to 9cm from the edge as a overlap to prevent the electric field distortion at the interface between the low-resistance anti-corona tape and the high-resistance paint from affecting the test. The schematic diagram of the short sample preparation is shown in the figure. Figure 5 shown.

[0182] Thermal aging tests were performed on the prepared samples. The wire rod samples were placed in a DHG-9640A electric constant-temperature forced-air drying oven with a maximum temperature of 200°C. During the thermal aging process, the oven temperature was set at 180°C, and the aging time was set at 0, 10, 20, and 30 days. PDC testing was performed immediately after each aging stage, with a polarization voltage of 3 kV and polarization and depolarization times of 300 seconds.

[0183] Branch parameter identification was performed on the depolarization current time series, and the branch parameters are shown in Tables 3-6. It is clear from the tables that with increasing aging time, the number of branches in the equivalent Debye model of the epoxy-mica insulation gradually increases, the branch relaxation strength also gradually increases, and the time constant gradually decreases. This is because long-term thermal aging gradually breaks the molecular chains of the macromolecular substances in the epoxy-mica insulation system, gradually degrading the substances into small molecules, thereby enhancing the material's conductivity and interfacial polarization.

[0184] Table 3 Identification results of thermal aging 0d

[0185]

[0186]

[0187] Table 4 Identification results of thermal aging for 10 days

[0188]

[0189] Table 5 Identification results of thermal aging for 20 days

[0190]

[0191] Table 6 Identification results of thermal aging for 30 days

[0192]

[0193] It can be seen that the R of the identification results under different aging conditions 2 Both are greater than 0.9950, and MAPE is less than 3%. It can be seen that in the laboratory environment where the noise level is lower than the field environment, the algorithm has good accuracy and robustness.

[0194] Those skilled in the art will appreciate that the embodiments described herein are intended to help readers understand the principles of the present invention, and it should be understood that the scope of protection of the present invention is not limited to such specific descriptions and embodiments. Those skilled in the art can make various other specific variations and combinations based on the technical teachings disclosed in the present invention without departing from the essence of the present invention, and such variations and combinations are still within the scope of protection of the invention.

Claims

1. A method for evaluating the insulation status of a high-voltage generator stator winding, characterized in that: The following steps are involved: S1: Establish an extended Debye model for high-voltage generator stator winding insulation; S2: Based on the dynamic modal decomposition algorithm, the depolarization current time series of the high-voltage generator stator winding is modally decomposed to obtain various modes with different physical meanings; The S2 includes the following steps: S21: Construct the depolarization current time series into a Hankel matrix, the formula is: in, is the Hankel matrix, is the depolarizing current sequence, is the number of rows of the Hankel matrix, is the number of columns of the Hankel matrix, is the number of depolarization current sampling points; S22: Based on the dynamic mode decomposition algorithm, take the front of the Hankel matrix Column and rear The columns constitute the leading matrix and the lagging matrix, and the relationship between the leading matrix and the lagging matrix is: in, is the leading depolarization current matrix, is the hysteresis depolarization current matrix, is the Koopman operator, is the residual matrix; S23: Perform singular value decomposition on the leading depolarization current matrix, and perform low-rank approximation on the Koopman operator based on the decomposition result, and construct a low-rank operator in the low-rank space; S24: Solve the eigenvalues ​​and eigenvectors of low-rank operators, and based on the solution, obtain the modes of different physical meanings of the extended Debye model of high-voltage generator stator winding insulation; S3: Based on the fast iterative shrinkage threshold algorithm FISTA, each mode is sparsified to separate the dominant mode from the false mode. The dominant mode solution is used to expand the Debye model and achieve accurate collaborative identification of the number of model branches and branch parameters. The S3 includes the following sub-steps: S31: Establish the initial amplitude coefficients of each mode; S32: Based on the initial amplitude coefficient, the fast iterative shrinkage threshold algorithm FISTA and the penalty function are used for sparsification to separate the dominant mode from the false mode; S33: Based on the separated dominant modes, the parameters of the extended Debye model are calculated to achieve accurate collaborative identification of the number of model branches and branch parameters. The formula is: in, For branch The time constant, is the sampling time interval of the PDC test, is the eigenvalue corresponding to the dominant mode, For branch The amplitude coefficient of S4: Based on the solution results, simulation and thermal aging experiments are performed using preset model parameters to complete the insulation status evaluation of the high-voltage generator stator winding.

2. The method for evaluating the insulation status of a high-voltage generator stator winding according to claim 1, wherein: The depolarization current of the extended Debye model in S1 is expressed as: in, is the depolarizing current, is the polarization voltage, For branch The resistance, is the number of relaxation branches, For time, is the relaxation time constant, For branch The current amplitude, is the polarization time, For branch capacitance.

3. The method for evaluating the insulation status of a high-voltage generator stator winding according to claim 2, wherein: In S23, the leading depolarization current matrix is ​​subjected to singular value decomposition, and the formula is: in, is a left singular matrix, is the singular value matrix, is a right singular matrix, the superscript represents the complex conjugate transpose of a matrix; Construct a low-rank Koopman operator in a low-rank space, the formula is: in, is a low-rank operator, is the left singular matrix after rank truncation , is the left singular matrix after rank truncation , is the singular value matrix after rank truncation .

4. The method for evaluating the insulation status of a high-voltage generator stator winding according to claim 3, wherein: In S24, the eigenvalues ​​and eigenvectors of the low-rank operator are solved, and the formula is: in, for The eigenvector matrix of for The diagonal matrix of eigenvalues; The modes of different physical meanings of the extended Debye model of the high-voltage generator stator winding insulation are: in, is the modal vector, For modal.

5. The method for evaluating the insulation status of a high-voltage generator stator winding according to claim 4, characterized in that: The S31 includes the following sub-steps: S311: Establish the expression of the leading depolarization current matrix including the initial amplitude coefficient, the formula is: in, is the leading depolarization current matrix, is the initial amplitude coefficient matrix, is the Vandermonde matrix containing the main insulation relaxation characteristics, is the transpose of the matrix, is the initial amplitude coefficient of each mode, is the eigenvalue corresponding to each mode; S312: Obtain the reconstruction error caused by the leading depolarization current matrix including the initial amplitude coefficient, solve the reconstruction error, and complete the establishment of the initial amplitude coefficient of each order mode. The reconstruction error is: in, is the reconstruction error, is the vector of each order modal amplitude coefficient, is the Frobenius norm, is the trace of the matrix, is the first parameter, is the second parameter, is the third parameter, To take the main diagonal elements of the matrix to form a column vector; Solve the vector of each order modal amplitude coefficient for: 。 6. The method for evaluating the insulation status of a high-voltage generator stator winding according to claim 5, characterized in that: The S32 includes the following sub-steps: S321: Use 1-norm as regularization penalty function to establish the objective function for optimizing the initial amplitude coefficients of each mode , the formula is: S322: The fast iterative shrinkage threshold algorithm FISTA is used to iteratively solve the objective function of optimizing the initial amplitude coefficients of each mode to eliminate false modes and achieve separation of dominant modes from false modes.

7. The method for evaluating the insulation status of a high-voltage generator stator winding according to claim 6, wherein: In S322, the fast iterative shrinkage threshold algorithm FISTA is used to iteratively solve the objective function of optimizing the initial amplitude coefficients of each mode, including the following steps: S3221: Calculated Set as the initial value of the iteration , set the initial value of the momentum term , set the initial value of momentum acceleration parameter , step length is the Lipschitz constant of the objective function; S3222: Perform gradient descent solution, the formula is: in, for Iteration No. The value of times, is the regularization penalty function At the point The gradient at is the momentum variable; S3223: Yes Perform soft threshold shrinkage to obtain the next iteration for: in, is the soft threshold function, is the threshold value of the soft threshold operation; S3224: Update momentum acceleration parameters for: in, is the updated momentum acceleration parameter ; S3225: According to and Update the momentum variable for the next step for: S3226: Momentum variable based on the next step , return to step S3222 and iterate until the convergence condition is reached, and then stop iterating. The convergence condition is: in, is the preset convergence threshold.

8. The method for evaluating the insulation status of a high-voltage generator stator winding according to claim 7, wherein: In the step S322, the amplitude of the false mode is set to zero to eliminate the false mode, so that each dominant mode corresponds to the branch of the extended Debye model. The formula is: in, is a matrix whose column vectors are unit vectors.

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